Sets can be changed by adding items (joining) or by taking some away (separating).

Many problem situations involve change—adding to or taking away from a set. Such changes lend themselves to concrete models or to acting out as sets are joined or separated and then counted to find out “how many now?”. However, it is also important for young children to make the more foundational generalization that adding increases and taking away decreases the quantity in a set.

Five Little Goldfish

"This is math, of course, but it's not math. It's a game. I keep it a game by not belaboring mathematical ideas or concepts. Yes, I use terms like 'addition' and 'subtraction' and 'equals,' when I can as part of the natural flow of things, because it's always good to introduce vocabulary words 'in context.' I support the kids in any way necessary to help them figure out how many fish they have."